What Is a Key?

(Written in 1996)

What does it mean to be playing music in a certain key?
Well, let’s start from the beginning…

What is sound?

A moving object exerts a force on air molecules, compressing them closer together under greater pressure. Delicate bones in our inner ears are moved (less than a thousandth of an inch) by the air pressure, and nerves pick up their motion and interpret it as sound. Vibrating objects like guitar strings, guitar soundboards, and speakers (or vocal cords) create periodic changes in air pressure, where it is alternately increased above the normal value (when there’s no sound) as they move toward you, and then decreased below the normal value as they move away from you. A periodic sound is also called a tone.

What is pitch?

The number of times that the air pressure changes in any given period of time determines what pitch we hear the tone as–how high or low the tone is. Each movement back and forth is called a cycle. Usually pitch is measured in cycles per second, also known as Hertz (named after a 19th century physicist). The pitch of a tone is also called its frequency, because it is determined by how often (frequently) the air pressure is changing, which is determined by the frequency at which the part of the instrument that created it was vibrating.

The middle A key of a piano is a string vibrating at 440 Hertz; that is the standard pitch that orchestras tune their instruments to, so tunings based on it are said to be in concert pitch.

What is an octave?

When a tone has a frequency that is twice as high as another tone, we hear it as being “the same note”, only an octave higher. The next A above the middle A on a piano is vibrating at 880 Hertz, and the next A below the middle A is 220 Hertz.

If one vibrating object (such as a piano or guitar string, or a reed) is half as long as another one that has the same thickness and is tightened to the same tension, that shorter object will vibrate at twice the speed as the other one–one octave higher than it. (I don’t know why it happens that way.) Therefore, the 12th fret of a guitar, which is one octave higher in pitch than the open string, is located in the middle of the string.

What is volume?

The amount of difference in the air pressure determines how loud we hear a sound as being. If the pressure changes are large, we hear a loud noise. So if the air molecules (and thus our eardrums) are vibrating rapidly but only a short distance, we hear a high-pitched but quiet sound.

Why do different kinds of instruments sound different?

The strings (or whatever is making the sound) aren’t only vibrating at one frequency. Although there is one fundamental frequency for each tone, the motions of the air particles are actually composites made up of vibrations of several frequencies. The frequency that has the biggest impact on the resulting air particle (and ear drum) motion is the fundamental frequency, which we perceive as being the pitch of the sound.

The other frequencies mixed in with it to varying extents are what give the instrument its timbre (pronounced “tamber”) — what makes a guitar sound different from a trumpet or a violin. Many of these other frequencies that are mixed in are actually multiples of 2 of the fundamental frequency, and the one an octave above is called the first harmonic, the one two octaves above is called the second harmonic, etc. When we play a guitar string while touching it at its halfway point, we are muting the fundamental frequency while emphasizing the first harmonic; similarly for one-quarter of the string length and the second harmonic, and so on.

How are octaves divided up?

In the music of Western civilization, an octave is divided into 12 notes; the exact locations of the divisions were decided on by J.S. Bach. These 12 notes together are called the chromatic scale, perhaps because they are the distinct “colors” with which we “paint” to create music (“chroma” usually refers to shades of pigment or light). Other civilizations, such as India and China, have developed systems of music that divide octaves into other numbers of notes. Why do we use 12 notes? Perhaps because 12 can be divided into half, and also into fourths, which makes writing melodies using that scale easier. But we actually use more notes than those 12; we make in-between notes when we bend strings for added expressiveness using our fingers or a vibrato bar.

Does a song use all of the chromatic notes?

Not usually, except in some experimental jazz music. Normally, a piece of music uses a subset of the chromatic scale. The notes of the chromatic scale are also called semitones; the intervals between them are called half steps. The notes on a guitar are all a half-step away from each of the two notes on the frets next to them on the same string. Going from one semitone to another, while skipping one semitone between them, is called a whole step (yes, it’s made up of two half-steps). That’s skipping a fret on a guitar.

Certain patterns of whole and half steps are commonly used; the most common is the major scale, which has the pattern “whole-whole-half-WHOLE-whole-whole-half”. To make it easier to remember the pattern, you can think of it as two “whole-whole-half” patterns separated by a whole step, which I capitalized to make it stand out. This organization within the major scale has no significance that I know of besides making it easier to remember the pattern. Why is this particular set of semitones used? It just seems to sound good. It has a “stable” feel to our ears. Some other popular scales are the harmonic minor scale and the pentatonic scale, which use different subsets of the notes of the chromatic scale.

How were the note names chosen?

The 8 notes of the C major scale (not A major, for some unknown reason) are referred to using the names of the first 7 letters of the alphabet (A through G), with the octave note having the same letter name as the root note (C). The remaining notes of the chromatic scale each have two names; you can think of them as being sharp (higher in pitch) compared to the chromatic note just below them in frequency, or flat (lower in pitch) compared to the note just above them. So the note between C and D can be called both “C sharp” and “D flat”.

Because of where the half steps happen to be in the major scale starting on C, there is no note between E and F or between B and C. So there is no “B sharp”, for example. Other scales, and the major scale starting in keys other than C, do contain some of those “sharp/flat” notes. The word “sharp” is usually abbreviated “#”, and “flat” is written as “b”, or a symbol that looks a lot like a “b”.

So, what is a key, then?

A key is the notes of a particular scale (e.g., major), starting on a particular note (e.g., C). A piece of music that is in a particular key, such as “C major”, has a melody that uses only (or mostly) notes in that scale. For unusual effects, it might have an occasional note that is not in that scale; these notes are called accidentals.

Where do the chords in a key come from?

A chord is just three or more notes played simultaneously. (Playing just two notes at once is called a double stop.) The chords that are naturally part of a given key are the chords that contain only the notes in that key’s scale. The intervals between the notes in a chord determine what kind of chord it is–the feeling that the sound of the chord has to our ears, as well as what name we give the chord.

If you start with the root note of the scale (C for the key of C major) and add the third and fifth notes of the scale, you have what’s called a a major chord. That is a three-note chord with a two-whole-step interval between the low note and the middle note, and a one-and-a-half step interval between the middle note and the high note. For example, a C major chord contains the notes “C E G”. Since a guitar has more than three strings, when we play a major chord on it we can double some or all of those three notes on different strings, perhaps in different octaves, for a fuller sound.

If you start on the third note in the key’s scale and add the third and fifth notes of that scale above the note you started with, you end up with a minor chord, which is a three-note chord with a one-and-a-half-step interval between the low note and the middle note, and a two-whole-step interval between the middle note and the high note. For example, in the key of C major, if you base a three-note chord on the third note of the C major scale (E) and count that note as “1”, then the “3rd” note is G and the “5th” is B. That’s an E minor chord, containing the notes “E G B”, and written “Em”.

You can occasionally use chords that contain notes that are not in the song’s key, when you want a sound that is less normal sounding. For example, a dominant 7th chord contains four notes, one of which is the flattened 7th scale note above its root: a G7 chord contains an F note, not the normal F#.

Why do we skip notes, and not play chords that consist of, say, the first, second, and third notes of a scale? Playing all those close-together notes doesn’t sound very good. But we do sometimes use one close interval by including an even-numbered note, for example in the C6 chord (C E G A). Perhaps the most common type of chord where this is done is Csus4 (C F G), in which the third is “suspended” (omitted) and the fourth is added.

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